Electrical wave band pass circuits



Cet. 6, 1953 E. c. CORK 2,654,867

ELECTRICAL WAVE BAND PASS CIRCUITS Filed Oct. 5, 1949 2 Sheets-Sheet 1 F/GZ.

EDWARD CEC/L CORK 5y @WCM Oct. 6, 1953 E; Q CQRK 2,654,867

ELECTRICAL WAVE BAND PASS CIRCUITS Filed oct. 5, 1949 2 sheets-sheet a 47 4e F/G. 4.

53 57 5i IIL I 59 /IJ ven for EDWARD CEC/L CORK Afin/wey Patented `ct.l 6, 1.9.5.3

Y 2,654,867 ELECTRICAL WAVE BAND PAss, CIRCUITS Edward Cecil Cork, Ealing, London, England,

assignor to Electric & Musical Industries Limited, Hayes, England, a company of Great Britain Application october 5, 1949, serial No. 119,617

, i, In GreatBritain October 1, 1948 This invention relates to electrical Wave bandpass circuits, f

In the Bell System Technical Journal'volume 16, 1937, pages 178 to 193, there is described the derivation of two finite networks which when connected in parallel form a band-pass circuit Whose input impedance is theoretically a constant resistance at all frequencies. Figure 1 of the drawings illustrates an electrical wave bandpass circuit constructed as described with reference to Figures 5 and 6 in the aforesaid publication, the same symbols having been used in Figure 1 as in the publication, with n howeverequal to 5 for convenience` of description. The values O ai scribed in the aforesaid publication, and as also described therein the quantities Pizand P22 are closely associated with the cut-off frequencies of the circuit, A is a symbol representing and the circuit has terminating resistances R which are normalised to a value of unity. The terminals and the branch points of the first of the networks in Figure 1 are denoted by the references l 8 and the terminals and branch points of the second of the networks are denoted by the references 9 I6. The impedances an ati are inductancesand ai/i as/k are condensers, that is, the series impedances are each reactances of one sign, whilst the impedances in each of the branches 3, 4; 5, 6; Il, l2; and I3, I4 form tuned circuits.

A circuit such as illustrated in Figure 1 is suited for applications involving the` transmission of low frequency electrical signals where the wave length is long compared with the physical dimensions of the components of the circuit. However when applications are considered involving the transmission of high frequency electrical signals, such as encountered for example in carrier wave television transmitters, Vseveral difficulties are encountered. For example the series impedances asi and as/x etc. are at high potential and ungrounded so that stray capacity to ground and phantom circuits affect the performance of the circuit, and the physical realisation of series impedances by means of transmission line sections is diiiicult. l The circuit components are difiicult to adjust and no mechanism exists in the circuit for attempting to annul stray capacities and inductances at junction points. Moreover, in the circuit illustrated the impedances are i theoretically disposed at one point in space, a

. a5 are determined in the manner de- 6 Claims. (Cl. 333-9) requirement which it is physically impossible to approach in constructing a circuit by means of transmission line sectionsl The main object of the present invention is to provide an improved electrical wave bandpass circuit with a view to overcoming the above described difficulties in a circuit whose input impedance is effectively a constant resistance.

A further object of the present invention is to provide an improved electrical wave band-pass circuit wherein, by the use of the transforming action of transmission line sections, a circuit `equivalent to alternate series and shunt impedances is provided by the employment of only shunt-connected mpedances, and wherein means are provided for `reducing the undesirable variation in the input admittance of the circuit due to variation in the electrical length of the sections with frequency.

The presen-t invention utilises the transforming action of a quarter wavelength transmission line whereby a shunt impedance preceded by a quarter wavelength line is equivalent to a series impedance which is the inverse of the shunt impedance with `respect to the characteristic impedance of the transmission line, over the range of frequencies for which the transformation is substantially accurate. It is therefore possible by a series of inversions of the impedances utilised in the circuit illustrated in Figure 1 to obtain a circuit which can be readily realised by means of transmission line sections and which nevertheless retains the property of having an effectively constant resistance over a range of frequencies.

In order that the said invention may be clearly understood and readily carried into effect, the same will now be more fullydescribed with refence to Figures 2 to 6 of the drawings in which:

Figure 2 illustrates diagrammatically one example of a band-pass circuit in accordance with the present invention,

`Figure 3 illustrates diagrammatically a practical realisation of this circuit employing co-axial transmission lines,`

Figure 4 illustrates another form of circuit constructed in accordance with the principle illustrated in Figure 2, and

Figure 5 is a diagrammatic representation of Apart of Figure 4.

Referring to the drawings, the circuit illustrated in Figure 2` comprises two networks, the

` terminals and branchpoints of the first of which are indicatedby the reference numerals ll accese? terminating impedance in Figure 1. The successive pairs of points on the conductors; Off Said. transmission line are separated by distances of a quarter wavelength at a predetermined free. quency w, a quarter wavelength being denoted on the drawings by the symbol Z/4 to avoid confusion with the previously dened symbol x. The

terminating resistance of the nework |1' 35.1l

connected between the terminals I1; and I3 is the inverse of the terminating resistance of the about w for which the transformations eliected are substantially accurate. It will be appreciated that the circuit illustrated can be applied to the general case of (2n-H) successive sections, in which case the co-efcients al@ ,y aan-l-I and P1 .P2 Pn are determined in the manner described in the aforesaid publication;

Figure 3 diagrammatically shows a practical 'realisation of the circuit illustrated in Figure 2 wherein concentric transmission line sections are employed to provide the shunt impedances. Corresponding vpoints in Figures 2 and 3 are indicated by the saine ref lrence numerals and in Figure 4 shunt impedances which are capacitative (i. e. those for which the symbol A appears in the .Y denominator) arev shown as open circuited secnetwork I 8 of Figure 1 with respect to the characteristic impedance of said transmission line and therefore in the present example has also the aforesaid value A shunt impedance is connected between the points I9, having the value obtained by inverting with respect to R the series impedance ai/A of Figure 1. Since the impedance to the right of thev points I9, 2D is inverted at 2 I', 22 by reason of the quarter wavelength section of transmission line between the points I9, 2 I the impedance to the right of points 2|', 22- in Figure 2 is identical to the impedance to the right of points 3, '4 in Figure 1, within the range offrequenc-ies about w for which the transformation is substantial-ly accurate, which will depend upon the frequency selectivity of the transmission line. Between the points 2| and 22 -a shunt circuit is inserted comprising impedances equal in value to those between the points, .3, 4 in Figurev 1 and the impedance to the right of the points 2|, 22 is inverted at 2,3. and 24 by the quarter wave sections Vof transmission line .between the points 2|, 23. A shunt impedance having the value l/aak which is, the inverse of the series. impedance an between the points 3 and 5- in. Figure 1f, is connected between the, pointsv 2.3,;Y

24 and vthe impedance to thev right,` ofY the points 23., 24, is invertedat, points '2.5, 2 5; by the. transmission linev .setoll between. the. POHS. 23, ,25 so. that the impedancev at the points 25,216. the same as. at. thepoints 54.3. Figure i1 Within thel above-mentioned limita. A, shunt. Glcuitis connected between the points4 V25, 2 5 comprising impedances equal in velue t0. the impedances between the points .5. 6 Figure 1., and .e shunt impedance, having the value.. llaa. is inverse of the series impedance ask in Figure` 1 is connected between. the peints. 21. and 2.8,.. It will .now be apnarelilt. that by reason of. the invertions. effected b5!v the4 transmissionline sections between theA points4 2,5, 21V and 29, 3| the input impedance of the network I1 30, at the point,

3| 44 is arranged to be equivalent to thel network 9 .A It of Figure'l. Therefore by connecting thev terminals, 29,I '43 and 3 0, 414, in Figure 2 as indicated the networks together form a circuit whose input impedance 'is eiectively a constant resistance over the range of frequenciesvf tions While those which are inductive (i. e. those for' which the symbol x appears in numerator) are shown as short circuit sections. The tuned Circuits in the branches 2|, 22 and 25, 26 are shown as shortcircuited sections which are arranged to have the requisite selectivity while the tuned circuts in the branches 35, 35 and 39, 40 are shown as open circuited sections. However it will be appreciated that, by making use of the known properties of transmission line sections, the shunt impedances which are shown as open circuited sections may be replaced by short circuited` sections of differentlength andviceversa as may be rnost convenient or as required by the circuit constants, the method of illustration i-n Figure 3 having been chosen for convenience in order to illustrate that corresponding branches in the networks I1 3) and 3| 44 have inverse properties. The fact that the shun-t impedances in the circuit described are spaced at intervals of quarter wavelength along a transmission ligne has the advantage that stray inductancesy and capacities arising at the junction points can be made largely self-cancelling and some control of these undesirable quantities can be obtained.

The form or the, invention illustrated in Figure 3, is especially applicable to4 teleVSQIl. tra-11S- mitters employing vestigial side band operation. For example, in such application the television transmitter, indicated diagrammatically nhlock form atY 4.5, is connected across the terminals 2:9, 3l) andV 43, .44 in parallel and the resistance R connected between the. points; I1 and L8. formsthe aerial load while, the resistancev R connected between the points. 3l', 32 is providedby a resistive load. The knetwerk .I1 3|)v is arranged to have a band-pass; characteristic such that", it

passes the side band frequencies which it is desired. toV broadcast. whilethe network 3| .A 44

' is. arranged to. have a band-pass characteristic Y such that itv passes. theI frequencies which it; is

desiredv to. dissipate. It will of course be appreciatedI that the invention may :find other applications and it will. also b e appreciated that` the number of shunt impedances. employed may:- be `widely'different` from that illustrated in-Figures 2 and 3 and that the terminating resista-nce R may haveV other forms than .those described..

In` the form of the circuit illustrated in Figure 4 which is also applicable to. feeding the aerial: of

a television transmitter employing vestigialside Vband operation, the modulated carrier wave signals to be* transmitted arefed. to the entrypoi-nt 46 of the-lter bymeansof a feeder 41, havingconnected across itv a parallel. resonant vcircuit-:.48

which takes thel form of short. circuitedvquarter wavelength line and vwhoseA function will.` be. re-

ferred to later. From 1 thejunction. point: the

aesaeegz signals .are fedin parallel to twdsequences of transmission line sections,- one sequence comprising the sections 49 and 50 and the other sequence comprising the sections and 52.V The sections 49 52 have each an electrical length of one quarter wavelength of the carrier frequency. A capacity 53 is connected in parallel across `the output end of the section 49 and a tuned circuit 54 is connected across the output end of the section 50. The capacity is in the form of two open circuited transmission line sections, as indicated. While the tuned circuit is in the form of a transmission line section short circuited at both ends and connected at an intermediate point to the quarter wave length of the carrier frequency. It`

can be shown that the selectivity of the tuned circuit, that is the rate of change of its admittance with frequency, is dependent upon the location of the tapping point, said location being selected to obtain the appropriate value for the co-efiicient P in the equivalent shunt branch across the ends of the section 59. The aerial load is connected across the output end of the section 50, said load being merely indicated by an arrow 56. An inductance 51, in the form of a short-circuited section, is connected across the output end of the section 5 I, while a tuned circuit 58 of similar construction to the tuned circuit 54 is connected across the output end of the section 52. A resistive load, which is indicated by the arrow 59, is also connected across the output end of the section 52. The capacity 53 is transformed by the section 49, assuming perfect transformation,

into a series inductance `at the entry point 46, while the inductance 51 is similarly transformed by the section 5| to appear at the entry point 46 as a series capacity. The resistive load thus dissipates the upper side band of the modulated carrier wave signals, while the aerial radiates the carrier and the lower side band.

Figure 5 illustrates the equivalent circuit of the part of the circuit shown in Figure 4, to the left of the entry point 46, similar notation to that employed in Figure 2 being utilised to indicate that Figure 5 can be regarded as a particular case of the more generalised circuit shown in Figure 2. The part shown dotted in Figure 5, is not actually included in the circuit shown in Figure 4, because the theoretical value of 1 aix, is sufficiently small to allow it to be omitted, and no transformation is required for the load 56 since it is equal to its inverse. The input admittance of the circuit illustrated inFigure 5 (omitting the part shown dotted) for an input signal of such wave length that the electrical length Q `of the sections 49 Vand 50 is less than 90 by a small angle d0 can be expressed by the equation i In this equation Z1 represents the impedances 54 and 56 in parallel, Z2 represents the impedance of 53, and Za and Zb represent respectively the characteristic impedances of the sections 49 and 6. whether'` Za equals Zh or not, the latter being the case in this example. `The second term represents therst order error arising due vto the -departure of 0 from 90 and in the general case is `of the nature of `a conductance and a susceptance in parallel. The conductance error is small and is neglected in the present example. To reduce the susceptanceerror, Za and Zh are arranged to be different and to have such values in relation to Z1 and Z2 that the susceptance error becomes zero at a frequency near the edge of the band-pass which the part of the circuit in question has to handle. The susceptance error is also zero when d0 is zero. Therefore, over the desired side band the susceptance error is made small. Part of the circuit-'to the right ofthe entrygpoint can be similarly analysed and the same expedient is. adopted `to reduce` the first order susceptance.- error term. In this way it is` arranged that the input impedance ofthe circuit at the entry point 4t is a` substantially constant resistance over the required range of frequencies despite` the: variations in theielectrical length of the transmission line sections with frequency. The tuned circuitV 48 is employed to minimise residua1 error: in theinput impedance at lthe entry point 46 due. for example, to imperfect cancellation of stray.' inductances and capacities arranged at the junc-` tion points of the circuit.

Theexpedient described for reducing the rst: order error in the input susceptance can also beapplied to Figure 3, since the analysis of Figure 5 (neglecting the dotted part) isevidently applicable to any sectionof the circuit shown in Figure 3.` Moreover if the first order `'conductance error is significant it is possible to choose the Values of Za and Zh relative to Zi and Zz to make the conductance error zero at `one frequency near the edge of the band-pass of the respective part of the circuit. "It will also be zero when do is zero, and the conductance error can thus be made small over a desiredrangeof frequencies. This of course does not allow Za and Zb tobe chosen with a view to reducing the susceptance error, but thisterm can then be reduced by introducing a tuned circuit whose selectivity slope is such as to compensate for this error.

WhatIclaimis:

1. An electrical` wave band-pass circuit comprising at least onepair of series-connected twoconductor transmission line sections having respectively input and outputends and each having an electrical length of 211-1 quarter wavelengths at one frequency in the pass band of the circuit, n being any positive integer, a reactive impedance connected between the conductors at the output end of the first of said sections,` a series resonant circuit tuned in said pass band and a terminating load connected mutually in parallel between -the conductors at the output end ofthe other section, the `characteristic impedances of said sections being different and related tothe shunt impedances at the ends of the respective sections-to substantially annul the `reactive component at the input end of the first section at a frequency in said pass band different from said frequency, due to variation in the electrical length of the sections from 2n-1 quarter wavelengths at said different frequency.

2. An electrical wave band-pass circuit comprising at least one pair of series-connected twoconductor transmission line sections .having respectively input and output ends and eachhaving an `electrical length of 211,-1 "quarter wavelengths at one frequency in the pass `band of the amasar 7, circuitu being :any pcsitiuerinteger, i'azieactive'impedance connected between the :conductors .at the output end of the first .of .said sections, a series resonant circuit tuned rin said lpass band 'and va terminating .load fconnected mutually :in `parallel between the conductors :at the `output .end of the other section, .fthe ch'aracteristic impedance of said .sections being different-and related Eto the shunt impedances .at the ends rof the respective sections tosubstantially ani-iull the yresistive component .at the input endl cffthef-first .section at a frequency in said'ipass lband .different 'from -sa-id frequency, dueto variationin the-electrical 'length of .the lsections yfrom .2n-l fquarter wavelengths at .the diiferentTirequencv.`

3. An .electrical vvwave band-'pass circuit -corn- Vpricing-ia pair of `inputterniinals,'twosequencesof series-connected transmission line sections "leading from said input terminals, -each section having :an electrical length of 2n-1 quarter wavelengths atene frequency 1in -thepass band of the circuit, n -being any positive integer, l'the line sections "having input rand output ends, limpedances each of whichfis a-reactanceof one'sign at all frequencies 'in the `lpass band 'of the circuit connected across 'the output ends 'of odd-numbered line rse'ctionsin `the sequences, lseries resonant 'circuits :tuned kin Vsaidpass-'band and vconnected across the output 'ends Dieven-numbered line sections of the sequences, a `resistive lload connected acrossthe outputend of the last line section 'in each sequence, the band-pass l,circuit being equivalent to two parallel Ynetworks each Comprising "at least vone series-connected 'reactance, at vleast Vone shunt-:connected series tuned circuit,'and .aiterminatine 1oa'cl,jthe network elements being jdhnension'ed 'to' provide a ,substantia-lly'constantiinput-resistance,at all frequencies in saidfpassfbarrd. y g

4; electrical wave 'band-pass' circuit comprisingfapair ofinputterminals, two sequences of series-"connected,transmission v'line sections leading fromsaidiinputterminals, eachsectionhavingl ain-electrical lengt-hof .2n-"1 quarter wavelengths at'one frequency `inth'e pass `band 'of vvthe circuit, nbeingfanypositive integenthe'line sectionshaving input andoutputends, impedanceseachof which is a reactance of one signlat allfrequencies inthe pass v'band 'of "the circuit connected across the outputends. of 'odd-'numbered line. 'sections4 in the sequences, Yseries resonant 4circuitsltunedin said pass 'band fand 'connected across .the output ends of even-'numbered line sections `of .the V.sequences, a resistivefload .connected1across -the output'end .of .the last line section Aineachsequence, the .band-pass circuit beingfequivalent-to two parallel networks each kcomprising .at least one series-connected. .reactance, .atleast lone shunt-connected .series tuned circuit@ and .a .terminatingload, the .network elements v'being e'. dimensioned V.to provide xaV substantially :constant input .resistance xat all .frequencies ein .-saidfpass band, ,and .the v.characteristic ximpedances of :the individual oline. sections -beingdimensionediin "rclation to .thecnetworkfelements connectedfacross the .output ends .off-tbe .respectivednezsedtionsfto reducersubstantially to'.zero,;at arfrequencyl in said pass band differentfromthe rstementioned frequency, a. reactiveicomponent which is added to the :input resistance due tc :variation in the electrical llelrxgthaof the line sections with frequency.

l5.xfA1f1 f electrical .wave .band-.pass .circuit acomprisingia-gpairnof input: terminals, .two sequences 8, of series-connected transmission line sections leading: cfronisaid :input terminals', .each section having .an electrical length of 2n-'1 quarter wavelengths at one frequency rin :the pass band of the circuit, vn being any ,positive integer, .the linenfsections having input aand output ends, impedances .each :of which is Ya Vreactance Aof :one sign at .all frequencies in the :pass .band -of the circuit y.connected across the output ends .of oddnumbered'line sections in the sequences, series resonant'fcircuits .tuned Ain .said `pass* band .and connected across tthe :output ends :of `.even-num-v bere'd line sections :of the sequences, a resistive load connected across 'the output endbf'lthe last line isection in'each sequence, the bandpass circuit being `eutuv'alent `rto two parallel networks each comprising .atzleast one series-connected `reactance, at deast one vshunt-:connected series tuned cir-cuit, and `a terminating load, the network'elements :being dimensioned to Vprovide a substantially constantzinputresistanceat all frequencies in said pass band, andthe characteristic impedances .of `zthe individual :line sections being diinensioned inirelation to the networkelements connected -across the :output .ends of Vthe .respecive .Eline sections 4to .reduce substantially to izero, at :a frequency in f said ,pass band idiierent 'from the rst-zrnentioned frequency, .a variable resistive :component which :is 'added to saidconstant input resistance due to variation 1in the yelectri- V cal length'of'the linefsections with frequency.

'6. An :electrical vwave .band-'pass circuit :comprising transmissionlinefsections each having an electricalilength of 2n-1V quarter .wavelengths at one ifrequency in thefpassband ofthe crcuium beingany positive integelgsaid line sections having respectively input and output ends and being ,connected in sequence, impedance elements shunt-.connectedfacross the output ends of said sections and including a reactance -of one sign 'References fcitesin'the sie :of this patent UNITED STATES PATENTS Number Name Date 2,214,041 Brown Sept. 10,1940 2,258,974 Dagnail Ocala, 194i 2,270,416 Cork ,`Jan. 20, 1942 2,281,621 .ff-tust May 5, 1942 .1234323394 .Fox .'Dec. 9, 1947 234335368 Johnson etal.- Dec. 30, 1947 2,438,367 Keister Mar. 23, 1948 .2,588,226 .Fox Mar. 41952 `FOREIGNiPATENTS Number 'Country .Date

A59m-17.4 'Great Britain Ju1y,18,4 1947 f OTHER .REFERENCES l 

